Subword histories and Parikh matrices

Abstract

Parikh matrices recently introduced give much more information about a word than just the number of occurrences of each letter. In this paper we introduce the closely related notion of a subword history and obtain a sequence of general results: elimination of products, decidability of equivalence, and normal form. We also investigate overall methods for proving the validity of such results. A general inequality of “Cauchy type” for subword occurrences is established.